Theorems · Theorem · order theory
Nat.floor_eq_iff
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] {a : R} {n : ℕ},
0 ≤ a → (⌊a⌋₊ = n ↔ ↑n ≤ a ∧ a < ↑n + 1)- Defined in
- Mathlib.Algebra.Order.Floor.Semiring
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_addproof · cited by 586
- Nat.floorstatement and proof · cited by 215
- FloorSemiringstatement and proof · cited by 179
- le_antisymm_iffproof · cited by 62
- Nat.le_floor_iffproof · cited by 24
- Nat.floor_ltproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- Complex.GammaSeq_tendsto_Gammaproof · cited by 2
- Nat.floor_eq_on_Icoproof · cited by 1
- NNRat.floor_castproof · cited by 0
- NNRat.intFloor_castproof · cited by 0
- Real.nat_floor_real_sqrt_eq_nat_sqrtproof · cited by 0